SOL PRACTICE EXAM #4 (GRADED)

ALGEBRA 2 2012

1. Which expression is equivalent to1

216x ?

A 1

28x

B 1

24x

C 1

216x

D 4x

2. Assuming 0x , which is equivalent to the

following expression?

2

1 2

x x

x x

F 1 2

x

x x

G 1

H 1x

x

J 1

x

x

3. Which quadratic expression has an x – intercept at

2?

F 2 4x

G 2 7 12x x

H 2 8 16x x

J 2 30x x

4. When completely factored, 3 22 8 24x x x is

equivalent to –

A 3 22 4 12x x x

B 22 4 12x x x

C 2 2 6x x x

D 2 6 2x x x

5. Which expression is equivalent to 7 29 x y z ?

F 7 1

2 23 x y z

G 2

273 x y z

H 7 1

2 29 x y z

J 2

279 x y z

6. Which is equivalent to 7 3 2 6i i ?

F 5 3i

G 5 9i

H 5 9i

J 9 3i

7. Perform the following operation for

24 54

8. Which of the following graphs represents a quadratic function?

A

B

C

D

9. Which is equivalent to 14 1i ?

F 1 i

G 1 i

H 2

J 0

10. Given 2g x x , what is f g x if

23f x x

?

A 2 10 25x x

B 2 25x

C 3 28 21 18x x x

D 2 5 6x x

11. Simplify the expression?

1

5

2

5

x

x x

x

x

F 1

2x

G 22

1

x

x

H 2

1

2

x

x

J 2x

12. What is the solution(s) to the equation below?

2 7 9 16x

13. Which order pairs represent the solution set to the

following nonlinear system of equation?

2

3 1

3 8

x

x x

A 0, 1 0,8

B 3,10 3,8

C 3,8 0,8

D 0, 1 3,10

14. A quadratic function, D (x), is graphed as follows:

The function D (x) has ─

F 0 Solutions

G 1 Solution

H 2 Solutions

J 3 Solutions

15. Which inequality best represents the graph

?

A x a

B x a

C x a

D x a

16. What equation has the same solution as

2 1?xg x

F 2 6x x

G 3x

H 22 1x

J 4 1x

17. What is the solution set of the equation 23 3 7 0 ?x x

A 1 5 3 1 5 3

,2 6 2 6

i i

B 1 5 3 1 5 3

,2 6 2 6

i i

C 3 5 3, 3 5 3i i

D 3 5 3, 3 5 3i i

4 9f x x18. Which function is the inverse of ?

F 19

4

xf x

G 19

4

xf x

H 14

9

xf x

J 14

9

xf x

19. What is the range of the function

1 2 ?f x x

A ,

B , 1 1,

C , 2

D 2,

20. What property is illustrated by the equation?

2 3 2 3 3x x

21. If2 7 1f x x x , what is 2 6f ?

F 10

G 12

H 229

J 59

22. Identify the equation of the horizontal and vertical

asymptotes of 2 5

3 1

xp x

x

Solutions:

23. What is the value of c for the given equation?

2

4

5 5

xc

x x x

A 1

5

B 2

5

5x

C 5

5x

D 4 x

Horizontal

Asymptote

Vertical

Asymptote

y = 13

x = 13

y = 23

x = 23

y = 32

x = 32

3 1 5x

3,0,3

2x

24. Which function has the domain of

,0 0, ?

F

G

H

J

25. The equation has

A One Negative & One Positive Solution

B One Positive Solution

C One Negative Solution

D No Solution

26. If x ≠ 0 and y ≠ 0, which is equivalent to the

following expression?

y x x y

x y

F x y

xy

G

2 2x y

xy

H

2 2x xy y

xy

J

2x y

xy

27. List the coefficient of the term of the

polynomial function with the following roots:

- 4, 5, 0

28. What is the range of the function 2

2f x x

when the domain is ?

A 1,4,25

B 25, 4,1

C 25,0,25

D 4,0,25

29. Which function has a positive horizontal

asymptote?

F

G

H

J

30. The graph of 2 13 9h x x x has −

A three solutions

B two solutions

C one solution

D no solutions

31. A function, J (x), is graphed as follows:

The function J (x) is −

F Exponential

G Rational

H Square Root

J Cube Root

32. If p varies jointly as q and r squared, and p = 225

when q = 4 and r = 3, then find p when q = 6 and

r = 8.

33. Which of the following function(s) have the same range?

34. Which list of five consecutive terms is an

arithmetic sequence?

A 1,4,7,11,14

B 29,22,15,8,1

C 1,3,9,27,81

D 32,16,8,4,2

35. The time it takes you to get to campus varies inversely as your driving speed. Averaging 20

miles per hour in bad traffic, it takes you 1.5

hours to get to campus. How long would the trip

take averaging 50 miles per hour?

F 2 hours

G 1.7 hours

H 0.6 hours

J 0.3 hours

36. What is the domain of the function

f x x c

A ,c c

B ,

C , c

D ,c

37. What is the solution for the following equation?

35

2

x

F 97

G 103

H 47

J 53

38. Given: 1

1

n

na a r

Which is the eighth term of the geometric

sequence for which the first term is 18 and

13

r ?

A 1

B 48

C 727

729

D 2

243

I

II

III

IV

V

4f x x

2 4f x x

3 4f x x

4f x x

4f x x

39. What are the zeros of the polynomial function

4 216f x x x ?

F 4,4

G 4,0,4

H 16,16

J

40. In 1800, the official census found the population

of the United States to be 5.3 million. In 1810, the

census found the population to be 7.8 million.

What was the approximate exponential regression

equation in the US during this period? (let x =

number of years after 1800)

A 5.3 1.04x

B 5.3 0.25x

C 2.5 10x

D 5.3 7.8x

41. Which of the following describes the end behavior

of 2 9x

g xx

as x approaches positive infinity?

F y approaches positive infinity

G y approaches negative infinity

H y approaches 0

J y approaches 1

42. Which graph does not represent a function with a

range of all real numbers?

A

B

C

D

43. Indicate the intervals where the graph is only

increasing throughout the interval.

44. Write 2 100x in logarithm form.

F log 100 2x

G log 2 100x

H 2log 100 x

J 100log 2x

45. How many different three-letter codes are there if only the letter A, B, C, D, and E can be used and

no letter is used more than once?

A 10

B 60

C 15

D 8

46. What are the y – coordinates for the solutions to

this system of equations?

2

2

2 0

2 6 2 4 0

x x y

x x y

F 0y and 3

4y

G 2y and 1

2y

H 3

4y and

1

2y

J 0y and 2y

47. The number of roofing nails of a given length is

normally distributed with a mean length of 0.75

inches and a standard deviation of 0.02 inches. In

a box containing 2500 roofing nails, how many

nails are more than 0.78 inches long? Round to

the nearest whole number.

I

II

III

IV

V

VI

2 x

2x

1 2x

1 1x

2 1x

2x

x

48. The concentration (in milligrams per liter) of a

medication in a patient’s blood as time passes is

given by the data in the following table:

Assuming a quadratic regression model exists,

what is the concentration of medicine in the

blood after 2.75 hours have passed?

A 1.5

B 6.5

C 22.5

D 30.5

49. Which family of functions has a parent function

of 1

f xx

?

F Linear

G Quadratic

H Cubic

J Rational

50. Which graph does not represent a function with an

inverse?

A

B

C

D

Time

(Hours)

Concentration

(mg/l)

0 0

0.5 78.1

1 99.8

1.5 84.4

2 50.1

2.5 45.6

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# Answer: Standard:

1 B AII.1

2 J AII.4

3 F AII.8

4 D AII.1

5 F AII.1

6 G AII.3

7 5 6i AII.3

8 C AII.6

9 H AII.3

10 A AII.7

11 H AII.1

12 x = 7, 11 AII.4

13 B AII.5

14 H AII.7

15 D AII.4

16 G AII.8

17 B AII.7

18 J AII.7

19 D AII.7

20 Distributive

21 F AII.7

22 y = 23, x = 1

3 AII.7

23 C AII.4

24 F AII.7

25 B AII.4

# Answer: Standard:

26 G AII.1

27 -1 AII.1

28 A AII.7

29 G AII.7

30 B AII.8

31 J AII.6

32 2400 AII.10

33 I, II, V AII.7

34 B AII.2

35 H AII.10

36 D AII.7

37 F AII.4

38 D AII.2

39 G AII.8

40 A AII.9

41 F AII.7

42 D AII.7

43 I, V AII.7

44 H AII.9

45 B AII.12

46 F AII.7

47 167 nails AII.11

48 A AII.9

49 J AII.6

50 B AII.7